# What is the period of f(theta) = tan ( ( 7 theta)/12 )- cos ( ( 7 theta)/ 4 ) ?

##### 1 Answer
Jan 25, 2017

The period is $= \frac{24}{7} \pi$

#### Explanation:

The period of the sum of 2 periodic functions is the LCM of their periods

The period of $\left(\tan \frac{7}{12} \theta\right)$ is $= \frac{\pi}{\frac{7}{12}} = \frac{12}{7} \pi$

The period of $\left(\cos \left(\frac{7}{4} \theta\right)\right)$ is $= \frac{2 \pi}{\frac{7}{4}} = \frac{8}{7} \pi$

The LCM of $\frac{12}{7} \pi$ and $\frac{8}{7} \pi$ is $\frac{24}{7} \pi$